Definition – Zeroes/roots of a function.

Definition

Given a function $f(x)$ , we say that $x^*$ is a root, or zero, of the function if

$\displaystyle{f(x^*) = 0}$

Notes

The term “root” of a function is the most common terminology. It is also important to note that a function may have multiple roots rather than just one. Ie, despite the definition “including” only one root, $\displaystyle{x^*}$ , a function will often have more than one root, which is especially true for polynomials.

Furthermore, note the use of the word function. We do not say “roots of an equation” as the roots are what we find when setting $f(x) = 0$ , which is an equation. I.e, the roots of the function are solutions to an equation.